A non elliptic spectral problem related to the analysis  of superconducting micro-strip lines

Anne-Sophie Bonnet-Bendhia; Karim Ramdani

Displaying similar documents to “A non elliptic spectral problem related to the analysis of superconducting micro-strip lines”

Spectral analysis in a thin domain with periodically oscillating characteristics

Rita Ferreira, Luísa M. Mascarenhas, Andrey Piatnitski (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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The paper deals with a Dirichlet spectral problem for an elliptic operator with -periodic coefficients in a 3D bounded domain of small thickness . We study the asymptotic behavior of the spectrum as and tend to zero. This asymptotic behavior depends crucially on whether and are of the same order ( ≈ ), or is much less than ( = < 1), or is much greater than ...

Product of exponentials and spectral radius of random k-circulants

Arup Bose, Rajat Subhra Hazra, Koushik Saha (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We consider × random -circulant matrices with → ∞ and = () whose input sequence { }≥0 is independent and identically distributed (i.i.d.) random variables with finite (2 + ) moment. We study the asymptotic distribution of the spectral radius, when = + 1. For this, we first derive the tail behaviour of the fold product of i.i.d. exponential random variables. Then using this tail behaviour result and appropriate normal approximation techniques, we...

Spectral analysis in a thin domain with periodically oscillating characteristics

Rita Ferreira, Luísa M. Mascarenhas, Andrey Piatnitski (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique

Lorenzo Brasco (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We generalize to the -Laplacian a spectral inequality proved by M.-T. Kohler−Jobin. As a particular case of such a generalization, we obtain a sharp lower bound on the first Dirichlet eigenvalue of of a set in terms of its -torsional rigidity. The result is valid in every space dimension, for every 1 ∞ and for every open set with finite measure. Moreover, it holds by replacing the first eigenvalue with more general optimal Poincaré-Sobolev constants....

Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin laplacian

Pedro Ricardo Simão Antunes, Pedro Freitas, James Bernard Kennedy (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the problem of minimising the th-eigenvalue of the Robin Laplacian in R. Although for = 1,2 and a positive boundary parameter it is known that the minimisers do not depend on , we demonstrate numerically that this will not always be the case and illustrate how the optimiser will depend on . We derive a Wolf–Keller type result for this problem and show that optimal eigenvalues grow at most with , which is in sharp contrast with the Weyl asymptotics for a...

Finite volume schemes for fully non-linear elliptic equations in divergence form

Jérôme Droniou (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the -Laplacian kind: -div(|∇∇) = ƒ (with 1 < < ∞). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.

Continuity of solutions of a nonlinear elliptic equation

Pierre Bousquet (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a nonlinear elliptic equation of the form div [(∇)] + [] = 0 on a domain Ω, subject to a Dirichlet boundary condition tr = . We do not assume that the higher order term satisfies growth conditions from above. We prove the existence of continuous solutions either when Ω is convex and satisfies a one-sided bounded slope condition, or when is radial: $a (ξ) = l (| ξ |) | ξ | ξ$ a ( ξ ) = l ( | ξ | ) | ξ | ξ for some increasing:ℝ → ℝ

Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization

Houman Owhadi, Lei Zhang, Leonid Berlyand (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ( ) coefficients. Our method does not rely on concepts of ergodicity or scale-separation but on compactness properties of the solution space and a new variational approach to homogenization. The approximation space is generated by an interpolation basis (over scattered points forming a mesh of resolution ) minimizing...

Minimising convex combinations of low eigenvalues

Mette Iversen, Dario Mazzoleni (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the variational problem inf{ () + () + (1 − − ) () | Ω open in ℝ, || ≤ 1}, for ∈ [0, 1], + ≤ 1, where () is the th eigenvalue of the Dirichlet Laplacian acting in () and || is the Lebesgue measure of . We investigate for which values of every minimiser is connected.

Universality in the bulk of the spectrum for complex sample covariance matrices

Sandrine Péché (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We consider complex sample covariance matrices = (1/)* where is a × random matrix with i.i.d. entries , 1 ≤ ≤ , 1 ≤ ≤ , with distribution . Under some regularity and decay assumptions on , we prove universality of some local eigenvalue statistics in the bulk of the spectrum in the limit where → ∞ and lim→∞ / = for any real number ∈ (0, ∞).